It does fade out on purpose. Also on the video. The only thing I can think of is it being cut just for time.. Who knows what reason there could be. This happens more often than you think.
There is also a fade out in the V2 - Virginity concert (Both audio and video, just like Hametsu ni Mukatte) when Yoshiki and Komuro play a piano 'battle.'
And if you have the Live Live Live CD at hand, you can also hear (or better, notice) that the acoustic version of Rose of Pain stops at the point where hide would play his guitar again with a fast riff in the original. (While in the concert; Tokyo Dome 'White Night' the verse IS played)
So all I can think of as a reason is the time. Maybe in reality it was a really long piano play, and they couldn't fit it all on the video/audio CD.
Best bet is to ask yoshiki hehe.
I hope that helped.